How do I integrate various open source web applications with my website?

I have to create a web application for chef management in PHP . Time is the constraint. So instead of coding it from scratch , I have chosen various open source web applications for billing management, inventory management etc.(for eg. Billing and client management software, Easy Appointment Scheduling With Easy!Appointments).

Now I am not able to understand the way to proceed further. Should these applications be installed on server ? Then how will they be integrated with the website. Should an API be generated? Can these applications be in java, python etc . language , will this language difference cause problem in integration .

Or somehow their code should be copy pasted to form a website?

Can someone please guide me how things proceed with the web development and what are the options.Please excuse me if my above queries are dumb. I am a beginner. Please help.